This paper proposes a six-dimensional hyperchaotic system based on the Cellular Neural Networks (CNN) theory. Numerical analysis of the Lyapunov exponential spectrum, bifurcation diagrams, and complexity methods reveals that the system has multiple coexisting attractors and high initial sensitivity, verifying its rich dynamics and making it highly valuable in secure communications. The circuit of the system was then designed and implemented using the Multisim circuit simulation software, and the experimental results agreed with the numerical simulation results, verifying the realistic feasibility of the system. Finally, a color image chunking encryption algorithm is designed with the DNA algorithm, using the chaotic sequence generated by the six-dimensional CNN as the secret key source and the Logistic chaos mapping to generate the private key again to achieve double encryption. Since the legend of the algorithm is generated from the plaintext image, the effect of “one image, one secret” can be realized. The results show that the encryption algorithm has a good effect, high dislocation of the encrypted image, low correlation between neighboring pixels, increased sensitivity to the key, and high complexity and security.